Statistical characteristics of evolution strategies

Abstract

Evolution Strategies (ES) are an approach to numerical optimization that show good optimization performance. The evolutionary behavior of ES has been well-studied on simple problems but not on large complex problems, such as those with highly rugged search spaces, or larger scale problems like those frequently used as benchmark problems for numerical optimization. In this paper, the evolutionary characteristics of ES on complex problems are examined using three different statistical approaches. These are (1) basic statistical measures at the function-value level, (2) Hotelling's T2 for measuring the balance of exploitation and exploration at the individual-code level and (3) principal components analysis at the individual-code level for visualizing the distribution of the population. Among many formulations of ES, the fast-ES and the robust-ES are adopted for the analyses.